Low noise amplifier

ABSTRACT

An amplifier for signal amplification, the amplifier comprising: a signal input arrangement; a signal output arrangement; a first transistor; a second transistor; and a third transistor, wherein: the first, second and third transistors are coupled to one another to form a transconductance cell, the transconductance cell is coupled to the signal input arrangement and the signal output arrangement, and the transconductance cell is operable to receive a first signal from the signal input arrangement, amplify the first signal and output an amplified first signal to the signal output arrangement. There is also disclosed a receiver incorporating the amplifier and methods of operating the amplifier.

This is a National Phase Application under 35 U.S.C. § 371 ofPCT/GB2016/053372 filed Oct. 31, 2016 (published on May 4, 2017 as WO2017/072533); which claims priority to Great Britain Application No.1519263.6 filed Oct. 30, 2015; Great Britain Application No. 1519262.8filed Oct. 30, 2015; Great Britain Application No. 1519350.1 filed Nov.2, 2015; and Great Britain Application No. 1519348.5 filed Nov. 2, 2015;all of which are incorporated by reference herein in their entirety.

TECHNICAL FIELD

This invention relates to a low noise amplifier, particularly for use inmm-wave applications, a method of operating the amplifier and a receiverincorporating the amplifier.

BACKGROUND ART

Recent Federal Communications Commission (FCC) regulations has freed upsome unlicensed millimeter-wave (mm-wave) frequencies [1]-[2]. Suchregulations stem from lower overcrowded spectrums and the increasingdemand of users for high data rate wireless communications and radarsensors. Receivers targeting microwave and mm-wave applications based onthe wireless metropolitan area network standards ranging from 10-66 GHz,ultra-wideband radar vehicular sensor from 22-29 GHz, and military radarfor unmanned aerial vehicle (UAV) from 35-37 GHz [3], etc. are essentialto achieve the user end demands. This frequency spectrum allocationstill encounters adjacent channel coexistence, similar to lowerfrequency spectrums, like radio astronomy at 23.6-24 GHz,industrial-scientific-medical (ISM) at 24.05-24.25 GHz, localmultipoint-distribution system (LMDS) at 31 GHz, and cloud radar at 35GHz [4]. In fact, it presents a dilemma for some sensitive frequencybands where overlapping exists. The design of silicon-based radiofrequency integrated circuit (RFIC) receiver front ends at thesefrequencies for wideband performance with simultaneously high gain andhigh linearity is very challenging.

Low-noise amplifier (LNA) plays a crucial role in achieving high gainand linearity over wide operating frequency ranges for these receivers.Active balun-LNAs are LNAs capable of providing differential outputsfrom a single-ended input and are important component in receivers.Various wideband active balun-LNAs on silicon at low frequencies, whichimplement active and passive feedback mechanisms to improve linearity,gain and phase errors mismatches, have been reported [5],[6]. However,employing active feedback comes at the expense of power and nonlinearityrendering the harmonics cancellation ineffective [6]. A linearizationtechnique based on derivative superposition and its improved derivativeversion tend to provide impressive input referred third order interceptpoint (IIP₃) [18], [20]. The derivative superposition methods useauxiliary N/PMOS path in weak inversion to cancel the third-ordernonlinear current of the main transconductance gain-stage path, thusenhancing IIP₃. Nonetheless, this improvement is subject to deter thesecond inter-modulation product (IIP₂) due to nonlinear cross termsbetween the two paths [18]. Further, current-mode balun-LNA basedcommon-gate common-source structures with bias control and outputconductance kept constant show optimum behavior for both noise andlinearity [14], [19]. Such constrain across wideband is costly in termsof power consumption and subject to process, voltage, and temperaturevariations. Another approach is making third inter-modulation IM3cancellation independent of frequency in bipolar junction transistor(BJT) [15]-[17]. A second-harmonic control with fully differential modeconfiguration using BJT devices facilitates frequency independent IM3cancellation [15]. In [16]-[17], IM3 cancellation happens due to currenthyperbolic tangent behavior from dual gated BJT devices in differentialand pseudo-differential modes added to the output. However, the cost isdoubled in noise and power consumption.

All of these techniques were implemented in designs operating below 2.4GHz. A 20 GHz balun-LNA using 0.25 μm SiGe BiCMOS technology wasreported in [7]. This balun-LNA [7] consists of a common-emitter gainstage followed by a single-to-differential output buffer stage using acommon-emitter common-base (CE-CB) structure with ac current source.This design suffers from very high phase and gain mismatches, thuslimiting the bandwidth. These works show a tradeoff between linearity,power consumption, and gain.

SUMMARY OF INVENTION

Aspects of the invention are recited in the accompanying claims.

One aspect of the invention provides an amplifier for signalamplification, the amplifier comprising: a signal input arrangement; asignal output arrangement; a first transistor; a second transistor; anda third transistor, wherein: the first, second and third transistors arecoupled to one another to form a transconductance cell, thetransconductance cell is coupled to the signal input arrangement and thesignal output arrangement, and the transconductance cell is operable toreceive a first signal from the signal input arrangement, amplify thefirst signal and output an amplified first signal to the signal outputarrangement.

Preferably, the transconductance cell is configured with the collectorterminal of the first transistor coupled to the base terminal of thesecond transistor and the emitter terminal of the third transistor.

Conveniently, the amplifier further comprises: a first inductor coupledto the emitter of the first transistor; a second inductor coupledbetween the collector of the first transistor and the base of the secondtransistor, wherein the first inductor and the second inductor arearranged to operate respectively as a first coil of a transformer and asecond coil of a transformer.

Advantageously, the transformer is configured to perform at least one ofincreasing the voltage gain of the amplifier and/or increasing thesignal bandwidth of the amplifier.

Preferably, the signal input arrangement comprises an impedance matchingcircuit which is coupled to the first transistor, the impedance matchingcircuit comprising the first inductor and a third inductor each coupledto the base of the first transistor.

Conveniently, the amplifier further comprises a fourth inductor coupledbetween the emitter of the third transistor and the collector of thefirst transistor.

Advantageously, the collector of the second transistor is coupled to theemitter of a fourth transistor, and wherein the first, second, third andfourth transistors are arranged in a common-emitter configuration.

Preferably, the base of the third transistor, the base of the fourthtransistor and a power supply input are coupled to one another.

Conveniently, the signal output arrangement comprises: a first outputportion coupled to the collector of the third transistor; and a secondoutput portion coupled to collector of the fourth transistor.

Advantageously, the first output portion includes a first pair of seriesconnected inductors and a first output terminal coupled to theconnection between the first pair of inductors, and wherein the secondoutput portion includes a second pair of series connected inductors anda second output terminal coupled to the connection between the secondpair of inductors. Preferably, the amplifier further comprises: a firstresistor coupled between the first output portion and the power supplyinput; and a second resistor coupled between the second output portionand the power supply input.

Conveniently, the inductance of the first pair of inductors is equal tothe inductance of the second pair of inductors.

Advantageously, the amplifier is configured to be operable with apassive mixer and a trans-impedance amplifier and the signal outputarrangement is coupled to a class AB amplifier.

Preferably, the first signal comprises at least one signal having afrequency of 22 GHz to 35 GHz.

Conveniently, the amplifier is constructed using a SiGe BiCMOS process.

The present invention provides an improved low noise amplifier withwideband characteristics, high linearity and low power consumption.

Embodiments of the invention incorporate some or all of the followingfeatures either individually or in any combination: alow-power-consumption wideband 0.18 μm BiCMOS active balun-LNA withlinearity improvement technique for millimeter-wave applications isproposed. The linearity technique utilizes constant Gm transconductancestructure with second-order intermodulation (IM₂) cancellation thatprovides robustness to input and output variations. The constant Gm isestablished with equal emitters' area ratios and proper base-emitterbiasing voltage; thus improving linearity. Furthermore, power saving isachieved using inductive coupling boosting the overall Gm structure andreducing the current consumption for the auxiliary gain stage. Themeasured balun-LNA's power gain between the input and two outputs are15.4 dB and 15.6 dB with input return loss greater than 8.7 dB. The gainand phase mismatches are less than 1.8 dB and 12°, respectively. Thebalun-LNA noise figures between the input and two outputs are less than5.8 dB and 7.09 dB at 35 GHz. The measured P1 dB's and IIP3's are morethan −14.8 and −6 dBm across 22-35 GHz, respectively, and the totalpower consumption is less than 9 mW drawn from 1.8V power supply.

One embodiment of the low noise amplifier is a 0.18 μm SiGe BiCMOS 22-35GHz active balun-LNA with high linearity and low power consumption.

The linearity improvement is attained using a new linearity techniquebased on a constant Gm-cell transconductance that forms the balun-LNAstructure of the embodiment.

The constant Gm-cell transconductance is established through equalemitters' area ratios of the balun-LNA embodiment. The constantsmall-signal Gm-cell transconductance remains independent of input andoutput variations under large-signal behavior and provides second-orderintermodulation (IM₂) cancellation, resulting in improved linearity.

The low power consumption is due in part to the coupled inductors usedbetween cascaded stages. The balun-LNA embodiment targets multi-standardmulti-channel receivers' applications ranging from 22-35 GHz thatrequire high linearity. Many microwave and mm-wave applications not onlycoexist, but also overlap each other on the same frequency spectrum,making the linearity the bottle neck for the receiver's dynamic range.

BRIEF DESCRIPTION OF DRAWINGS

In order that the present invention may be more readily understood,reference is made by way of example to the following drawings, in which:

FIG. 1. shows a schematic of a low noise amplifier in a balun-LNA.

FIG. 2. shows the small signal model of the balun-LNA's input impedance.

FIG. 3. shows a comparison of magnitudes of Z′_(B) with and withouttransformer.

FIG. 4. shows the linearity model analysis for the conventionalcommon-emitter gm stage as well the balun-LNA embodiment Gm structureincluding the effect of the transformer.

FIG. 5. shows comparison curves for (a) Cascode LNA, (b) balun-LNA withtransformer, (c) balun-LNA without transformer.

FIG. 6. shows the noise source model of the balun-LNA embodiment.

FIG. 7. shows NF values for the differential output of the balun-LNAembodiment with ideal coupling coefficient; K; and transformer multipleturns n.

FIG. 8. shows a stacked transformer layout structure and its schematic.

FIG. 9. shows inductance values; L_(e1), L_(b2), and couplingcoefficient K, for stacked transformer using IE3D.

FIG. 10. shows a die photograph of the balun-LNA embodiment.

FIG. 11 shows the measured and simulated input return losses (S₁₁) forthe balun-LNA.

FIG. 12 shows the measured and simulated output return losses S₂₂ andS₃₃.

FIG. 13 shows S₂₁ and S₃₁ with a gain of 15.6 dB and 15.4 dB.

FIG. 14 shows the measured stability of the balun-LNA embodiment interms of the stability parameter μ, derived from the measuredS-parameters.

FIG. 15 shows the measured noise figures for both channels.

FIG. 16 shows the measured gain and phase imbalances.

FIG. 17 shows the measurements of the 1-dB power compression points (P1dB₂₁ P1 dB₃₁) and the input referred third order intercept points(IIP3₂₁ and IIP3₃₁) for both channels for the frequency range of 22-35GHz.

FIG. 18 shows a receiver chain for microwave and mm-wave coexistentapplications 22-44 GHz.

DETAILED DESCRIPTION

FIG. 1 shows a schematic of an embodiment of a 22-35 GHz(single-to-differential) wideband active balun and Low Noise Amplifier(LNA) with high gain, high linearity, and low power consumption.

Embodiments of the invention are described in detail below in relationto specific figures. The features disclosed in this description inrelation to a specific embodiment or in relation to a specific figureare not restricted to adoption in only that embodiment or in only thatfigure. Such features described in relation to a particular embodimentor in relation to a specific figure may also be adopted in otherembodiments or in connection with other figures unless there is aspecific technical conflict between the embodiments or figures.Accordingly, the features recited in the description are embodied in theinvention, as appropriate, either separately in relation to a particularembodiment or in relation to a specific figure, or in any combination ofsuch features.

The balun-LNA embodiment architecture of FIG. 1 consists of a maintransconductance gm gain stage, Q₁, coupled to an auxiliary gain path,Q₂, through a transformer. The coupled transformer increases the signalswing at the input of the second stage, thus boosting the Gmtransconductance, hence gain, and reducing the power consumption. Thecomposite Gm cell defined by transistors Q₁, Q₂, and Q₃ plays a majorrole in improving the linearization of the structure. The stipulatedtotal Gm stays constant even in the presence of variations in gm₁ of Q₁and gm₂ of Q₂ due to high input power. As the collector currents oftransistors Q₁ and Q₂ vary from their quiescent bias under large voltageswing; the gm's dependency on equal emitters' area (A_(e)) ratios keepsthe overall Gm-cell constant. The overall Gm's constant andfrequency-independent characteristic behavior with IM2 cancellationresults in linearity enhancement.

A simple wideband input matching network is established using inductorsL_(b) and L_(e1) similar to [10]. Preferably, the signal inputarrangement comprises an impedance matching circuit Xmr which is coupledto first transistor Q₁, the impedance matching circuit Xmr comprising afirst inductor L_(e1) and a third inductor L_(b2) each coupled to thebase of first transistor Q₁. First inductor L_(e1) is directly coupledand third inductor L_(b2) is inductively coupled to the base of firsttransistor Q₁. The effect of the coupling transformer (L_(e1), L_(b2))on the input matching is considered thoroughly in the later in thedescription. Inductive shunt peaking is used at the output loads (outputportions) to extend the matching bandwidth of the balun-LNA.

The noise due to the cascode transistor Q₃ is reduced by adding aninductor L_(m) to resonate away the parasitic capacitance at theemitter, thus reducing the output noise.

Input Matching Network

FIG. 2 shows the small-signal input impedance of the balun-LNA derivedfrom its schematic in FIG. 1. g_(m) is the small signal transconductanceof Q₁. R_(eq2) is defined as ω_(T)L_(e2) of Q₂, I_(p) and I_(s) are theprimary and secondary currents of the transformer.

To keep the analysis simple; the input impedance of the balun-LNA issplit into two sections Z_(B) and Z′_(B), which represent the inputimpedances looking into the respective networks. Under the perfectmatching condition, Z_(B)=Z′*_(B). Z_(B) forms a pi-network withwideband matching characteristics, whose quality factor (Q) reduces dueto the loading of the network represented by Z′_(B). For the ac coupledtransformer (L_(e1) and L_(b2)) in Z′_(B), the coupling coefficient Kand the number of turn n can cause the optimum matching point to shift;yet keeping wideband impedance matched to the input port. To study thiseffect, an expression for the complex conjugate impedance Z′*B isderived. Z′*B is found using the small-signal model in FIG. 2 whereasthe adapted transformer model is similar to that in [13]. ApplyingKirchhoff current law (KCL) at nodes E₁, C₁ and B₂, where M is themutual inductance;

$K = \frac{M}{\sqrt{L_{P}L_{S}}}$is the coupling coefficient, and n=√{square root over (L_(P)L_(S))} isthe turn ratio of the ac coupled transformer, can lead to Z′*_(B).C_(pad) is defined as the parasitic capacitance due to RF pad on chip.C_(be), C_(be2), and C_(be3) are the parasitic capacitances at thebase-emitter junctions of transistors Q₁, Q₂, and Q₃, respectively.Additionally, C_(he), and C_(p2) are the capacitances at thebase-collector junction of transistors Q₁ and Q₂. The KCL equationsyield, after several manipulations:

$\begin{matrix}{{V_{B}^{\prime}(s)} = {{{i_{B}^{\prime}(s)}\left( {1 + {\frac{1}{{sC}_{be}}\left( {1 + {{sg}_{m}L_{e\; 1}}} \right)}} \right)} - {MsI}_{s}}} & (1)\end{matrix}$where V′_(B) (s) is the base voltage looking into Z′_(B) network port,and i′_(B)(s) is its current defined as i′_(B)(s)=sC_(be)v_(be).

The secondary current I, of (I) can be derived as

$\begin{matrix}{{I_{s} = {{i_{B}^{\prime}(s)}\left\lbrack \frac{{g_{m}Z_{1}} - {{sM}\left( {{sC}_{be} + g_{m}} \right)}}{{sC}_{be}\left( {Z_{1} - {sL}_{b\; 2} - Z_{2}} \right)} \right\rbrack}}{where}} & (3) \\{Z_{1} = {{sL}_{m} + \frac{1}{g_{m\; 3} + {sC}_{{be}\; 3}}}} & (4) \\{Z_{2} = \frac{\left( {\frac{1}{{sC}_{{be}\; 2}} + {sL}_{e\; 2} + R_{{eq}\; 2}} \right)}{1 + {1/{{sC}_{p\; 2}\left( {\frac{1}{{sC}_{{be}\; 2}} + {sL}_{e\; 2} + R_{{eq}\; 2}} \right)}}}} & (5)\end{matrix}$

Substituting I_(s) into V′_(B)(s) and taking the ratio between (1) and(2) gives

$\begin{matrix}{{Z_{B}^{\prime}(s)} = {1 + {\frac{1}{{sC}_{be}}\left\lbrack {1 + {{sL}_{e\; 1}\left( {g_{m} - \frac{{s({Kn})}g_{m}Z_{1}}{Z_{1} - {sL}_{b\; 2} - Z_{2}} + \frac{{s^{2}({Kn})}^{2}{{sL}_{e\; 1}\left( {g_{m} + {sC}_{b\; e}} \right)}}{Z_{1} - {sL}_{b\; 2} - Z_{2}}} \right)}} \right\rbrack}}} & (6)\end{matrix}$

Z′_(B)(s) shows that any changes in the coupling coefficient K or thenumber of turn ratio n for the coupled transformer can affect the polesand zeros alike; thus causing the matching to shift into higherfrequency; yet maintaining the wideband characteristics due topoles-zeros cancellation effect.

FIG. 3 shows the schematic level simulation for the magnitude ofZ′_(B)(s) with and without the transformer, It is clear that thewideband matching characteristic is maintained with only small variationless than 2Ω in the worst case.

Low Noise Amplifier Linearity

FIG. 4(a) shows the linearity model analysis for the conventionalcommon-emitter gm stage. Using Taylor series expansion approximation,the output collector current for the CE stage is given by

$\begin{matrix}{i_{C} \cong {{gm}\left\lbrack {\sum\limits_{{q = 1},2,\ldots}^{\infty}{\frac{V_{T}}{q!}\left( \frac{v_{i\; n}}{V_{T}} \right)^{q}}} \right\rbrack}} & (7)\end{matrix}$where gm=I_(Q1)/V_(T), with I_(Q1) being the quiescent current of Q₁ andV_(T) being the thermal voltage, is the voltage to current conversionalso known as the small signal transconductance gm; and v_(in) is theinput voltage. From (7), taking the q^(th) order derivatives of gm withrespect to v_(in) encompasses all nonlinearities for the CE stage.Assuming v_(in)=V_(α) cos(ωt) and taking the ratio between the secondand the fundamental harmonic amplitude in a CE stage gives thesecond-order harmonic distortion as

$\begin{matrix}{{HD}_{2} = {\frac{1}{4}\left\lbrack \frac{V_{a}}{V_{T}} \right\rbrack}} & (8)\end{matrix}$

The collector currents in the proposed Gm stage for the balun-LN A asshown in FIG. 4(b) can be derived using (7) as

$\begin{matrix}{\mspace{20mu}{{i_{C\; 1} \cong {I_{Q\; 1}\left( {\frac{v_{i\; n}}{V_{T}} + {\frac{1}{2!}\left( \frac{v_{i\; n}}{V_{T}} \right)^{2}} + {\frac{1}{3!}\left( \frac{v_{i\; n}}{V_{T}\;} \right)^{3}} + \ldots}\mspace{14mu} \right)}}{i_{C\; 2} \cong {I_{Q\; 2}\left( {\frac{v_{2}\left( {1 + {nK}} \right)}{V_{T}} + {\frac{1}{2!}\left( \frac{v_{2}\left( {1 + {nK}} \right)}{V_{T}} \right)^{2}} + {\frac{1}{3!}\left( \frac{v_{2}\left( {1 + {nK}} \right)}{V_{T}} \right)^{3}} + \ldots}\mspace{14mu} \right)}}\mspace{20mu}{i_{C\; 3} \cong {I_{Q\; 3}\left( {\frac{- v_{2}}{V_{T}} + {\frac{1}{2!}\left( \frac{- v_{2}}{V_{T}} \right)^{2}} + {\frac{1}{3!}\left( \frac{- v_{2}}{V_{T}} \right)^{3}} + \ldots}\mspace{14mu} \right)}}}} & (9)\end{matrix}$

Using (9), we find the differential output current i_(Out)=i_(C3)-i_(C2)with respect to the input voltage v_(in) assuming i_(C1)=i_(C3) andusing the fact that −v₂/v_(in)=−gm₁/gm₃=−A_(e1)/A_(e3), where A_(e1) andA_(e3) represent the emitter area for Q₁ and Q₃; respectively, as

$\begin{matrix}{i_{Out} = \begin{bmatrix}{{{I_{Q\; 3}\left( \frac{{- \left( {A_{e\; 1}/A_{e\; 3}} \right)}v_{i\; n}}{V_{T}} \right)}\left( {1 + \frac{I_{Q\; 2}\left( {1 + {nK}} \right)}{I_{Q\; 3}}} \right)} +} \\{{\frac{I_{Q\; 3}}{2}\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)v_{i\; n}}{V_{T}} \right)^{2}\left( {1 - \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{2}}{I_{Q\; 3}}} \right)} +} \\{{\frac{I_{Q\; 3}}{6}\left( \frac{{- \left( {A_{e\; 1}/A_{e\; 3}} \right)}v_{i\; n}}{V_{T}} \right)^{3}\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)} + \ldots}\end{bmatrix}} & (10)\end{matrix}$

Substituting v_(in)=V_(α) cos(ωt) into (10) results in

$\begin{matrix}{i_{Out} = \left\lbrack {{\left\lbrack \left( {I_{Q3}\left( \frac{{- \left( {A_{e\; 1}/A_{e\; 3}} \right)}V_{a}}{V_{T}} \right)} \right) \right\rbrack\left( {\left( {1 + \frac{I_{Q\; 2}\left( {1 + {nK}} \right)}{I_{Q\; 3}}} \right) - {\frac{1}{8}\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right)^{2}\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)}} \right)\cos\;\varpi\; t} + {\frac{I_{Q3}}{4}\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right)^{2}\left( {1 + {\cos\; 2\omega\; t}} \right)\left( {1 - \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{2}}{I_{Q\; 3}}} \right)} + {\frac{I_{Q3}}{24}\left( \frac{{- \left( {A_{e\; 1}/A_{e\; 3}} \right)}V_{a}}{V_{T}} \right)^{3}\left( {\cos\; 3\;{\omega t}} \right)\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)} + \ldots} \right\rbrack} & (11)\end{matrix}$

From (11), considering the ratios between the second, and thefundamental amplitude harmonics as well between the third and thefundamental amplitude harmonics for the proposed Gm stage givesHD_(2,Gm) and HD_(1,Gm) respectively, as

$\begin{matrix}{{HD}_{2,{Gm}} = {\left( \frac{\left. {\left( \frac{1}{4} \right)\left( \left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right) \right)\left( {1 - \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{2}}{I_{Q\; 3}}} \right)} \right|}{{\left( {\left( \frac{1}{8} \right)\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right)^{2}} \right)\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)} - \left( {1 + \frac{I_{Q\; 2}\left( {1 + {nK}} \right)}{I_{Q\; 3}}} \right)} \right)}} & (12) \\{{HD}_{3,{Gm}} = \frac{\frac{1}{24}\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right)^{2}\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)}{\left( {\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{\;}}{I_{Q\; 3}}} \right) - {\frac{1}{8}\left( \frac{\left( {A_{e\; 1}/A_{e\; 3}} \right)V_{a}}{V_{T}} \right)^{2}\left( {1 + \frac{{I_{Q\; 2}\left( {1 + {nK}} \right)}^{3}}{I_{Q\; 3}}} \right)}} \right)}} & (13)\end{matrix}$

As can be seen from (12), the cancellation of the nonlinearity torgenerated due to HD_(2,Gm) is obtained under the conditionI_(Q2)(1+nK)²=I_(Q3) which means

$g_{m\; 2} = \frac{g_{m\; 3}}{\left( {1 + {nK}} \right)^{2}}$and in turn, V_(BE3)≈V_(BE2) and A_(e2)=A_(e3).

Hence, the overall Gm stays constant even in the presence of variationsin gm₁ and gm₂ due to large input voltage signal. As the collectorcurrents differ from their quiescent bias under large input power; thegm's dependency on the emitter area ratios keeps the overall Gmconstant. This large signal constant gm characteristic results inlinearity improvement. As HD_(3,Gm) from (13) cannot be cancelled,equation (13) dictates the linearity limitation for this proposedarchitecture. However, there is a clear tradeoff between gain andlinearity for this balun-LNA architecture. Keeping the aspect ratiosA_(e2)=A_(e3)=A_(e4) and

$g_{m\; 2} = {\frac{g_{m\; 3}}{\left( {1 + {nK}} \right)^{2}} = g_{m\; 4}}$between Q₂, Q₃ and Q₄ maximize the linearity at the expense of gain dueto

$G_{m} = {\left( {g_{m\; 1} + {\left( {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right)g_{m\; 2}}} \right).}$

Also, the gm₂ transconductance increases due to the transformer'sproduct nK which help boost the gain for less dc current. However, giventhe transformer inductors' sizes and the limited nK value the linearitydegradation is very small as depicted in FIG. 5.

The latter shows the simulation results of the input referred IdB gaincompression for a cascode LNA and the proposed balun-LNA with andwithout transformer. All circuits consume 6.4 mA current from a 1.8Vsupply and achieve 16-dB power gain. The P1 dB for the regular cascadeLNA and the proposed balun-LNA with and without transformer are −17.9dBm, −13.37 dBm and −13.26 dBm, respectively. The linearity improvementof the balun-LNA with transformer as compared to the cascade LNA isbetter than 4.53 dB.

Noise Analysis

The noise of the proposed balun-LNA is dominated by the input stageincluding the matching network and its auxiliary path. FIG. 6 shows thecircuit's main noise sources for the proposed balun-LNA. The noisesources include base and collector noise currents of Q₁ and Q₂. Noisedue to the parasitic base resistances R_(bx) and R_(bx2) of Q₁ and Q₂,respectively, and noise due losses of L_(b), R_(Lb), and couplingtransformer L_(ei) and L_(b2), R_(Le1) and R_(Lb2), is considered in thenoise model. The noise due to the cascade transistor Q₃ is considerablyreduced due to inductor L_(m) rendering the degenerated impedance highat resonance, thus making its noise contribution negligible [10].Furthermore; noise in the auxiliary path due to cascade transistor Q₄ isneglected due to multi-cascaded transconductance gain stages and, as aresult, all cascade transistors are neglected in the following analysis.

The equivalent input-referred noise due to the base and collectorcurrent shot noise of Q₁, Q₂, and its base parasitic resistance R_(bx2)are given by the equations (A8)-(A12) discussed later in thedescription. According to (A8) and (A9), the input referred noises of Q₁increases proportionally with L_(b)inductor's loss. This is because thesignal to noise ratio (SNR) between the input and the emitter-basejunction is inversely proportional to L_(b). It is clear that there is atradeoff between the input matching requirement for power transfer andthe noise figure for this balun-LNA embodiment structure. However,equations (A8)-(A9) reflect the effect of the coupling transformer onthe emitter impedance Z_(e) of Q₁. A higher Z_(e) helps improve thecollector current noise at the expense of lower (SNR) at theemitter-base junction. Similarly, equations (A10-A12) show an increasein the SNR at the base-emitter junction of Q₂ raising the voltage gainthrough the coupling transformer by (nk) factor. The collector shotnoise of Q₂ and its parasitic base resistance noise R_(bx2) are improvedby the same factor.

The total input referred voltage noise due to Q₁ and Q₂ √{square rootover (v² _(ni.Q) _(1.2) )}, normalized to the noise voltage sourceimpedance is given by

$\begin{matrix}{\sqrt{\frac{v_{{ni},Q_{\;{1,2}}}^{2}}{4{kTR}_{S}\Delta\; f}} \approx {\frac{\Psi_{1}(\omega)}{g_{m\; 1}} + {\left( {\Psi_{2}(\omega)} \right)g_{m\; 1}} + \frac{\Psi_{3}(\omega)}{\left\lbrack {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack} + {{\left( {\Psi_{4}(\omega)} \right)\left\lbrack {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack}g_{m\; 2}} + \frac{\Psi_{5}(\omega)}{\left\lbrack {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack g_{m\; 2}}}} & (14)\end{matrix}$ψ₁(ω)-ψ₅(ω) are given by the equations (A13)-(A17). This result showsthat the collector current shot noise of Q₁ and Q₂ can be improved byincreasing gm₁, gm₂ and transformer's product nK, respectively. However,such improvement comes at the expense of degrading the base current shotnoise. Hence, there is an optimum value for gm₁ and gm₂ to minimize thetotal input-referred noise voltage due to Q₁ and Q₂. Differentiating thefirst two terms and the last two terms of (14) with respect to gm₁ andgm₂ respectively and equating the resultant expressions to zero, resultsin gm_(1.opt) and gm_(2.opt), given by

$\begin{matrix}{g_{{m\; 1},{opt}} = \sqrt[\;]{\frac{\Psi_{1}(\omega)}{\Psi_{2}(\omega)}}} & (15) \\{g_{{m\; 2},{opt}} = {\sqrt[\;]{\frac{{\Psi 5}(\omega)}{{\Psi 4}(\omega)}}\frac{1}{\left\lbrack {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack}}} & (16)\end{matrix}$

The third term in (14) is due to the parasitic base resistance noise,R_(bx2) is limited by gm_(1,opt), A_(e2) emitter area of transistor Q₂,and the transformer coupling factor (nK). The total input referred noisefigure of the proposed balun-LNA structure is given by

$\begin{matrix}{{{NF}_{tot}(\omega)}❘{\approx {1 + {\frac{R_{L_{b}} + R_{bx}}{R_{S}}\left( {1 + {\omega^{2}C_{pad}R_{S}}} \right)} + {2\sqrt[\;]{{\Psi_{1}(\omega)}{\Psi_{2}(\omega)}}} + \frac{\Psi_{3}(\omega)}{\left\lbrack {\frac{1}{g_{m\; 3}}\sqrt[\;]{\frac{\Psi_{1}(\omega)}{\Psi_{2}(\omega)} + {nk}}} \right\rbrack} + {2\sqrt[\;]{{\Psi_{4}(\omega)}{\Psi_{5}(\omega)}}}}}} & (17)\end{matrix}$

FIG. 7 shows the noise figure simulations for the differential output ofthe balun-LNA. From (17); it is clear that signal to noise ratio (SNR)degradation between the source generator and the base-emitter junctioncapacitance is due to matching inductance loss L_(b), R_(Lb), theparasitic base resistance, R_(bx), and pad capacitance, C_(pad)Furthermore, an increase in the turn ratio of the coupling transformercould improve the noise figure.

However, the turn ratio cannot be increased randomly considering thecoupling transformer non-idealities [21]. Losses associated withparasitic resistances and capacitances at the base of Q₂ measuresquadratically compares to the secondary inductance of the transformer.Hence, the self-resonance frequency of the inductance suffers as well asthe magnetic coupling, M, reflecting higher noise. Ultimately, there arepractical limits for the voltage gain boosting effect and the optimalturn ratio n; thus achieving the lowest noise figure.

Stability and Power Efficiency

The effects of capacitors C_(bc) and C_(p2) on both channels are reduceddue to the cascade structure. The added transistors, Q₃ and Q₄,transform the input impedances of the driving stages from negativeimpedances into a capacitive one; hence the stability is maintained. Thetransformer is designed in inverting configuration to provide gainboosting without compromising the balun-LNA stability.

The proposed balun-LNA structure having dual g_(m), output from asingle-ended input combines the LNA characteristic with the balunbehavior into a single block. The inverting coupling transformer boostsg_(m2) by (nK) factor. This topology has two properties:

-   -   1) it can further boosts the voltage gain at the base-emitter        junction, thus reducing the dc bias point for a specific gain        target which means less dc power consumption, and    -   2) by controlling the coupling coefficient polarity, K, through        proper layout of the stacked transformer, the voltage gain can        be increased (with positive K) or remains the same with        bandwidth extended (for negative K).        Transformer and Inductor Layout

The presence of the parasitic capacitors and resistive losses generatedfrom routing paths in integrated circuits causes lower quality factor inpassive components, which could be significant at millimeter-wavefrequencies. To accurately account for such effects, all inductors aresimulated using electromagnetic (EM) simulator IE3D [22]. InductorsL_(d1), L_(d3), and L_(b) are designed using spiral inductor due totheir relatively large inductances. However; a careful consideration isbeing assigned for the metal width trading off the resistive loss,parasitic coupling to the substrate, quality factor and inductorsself-resonance frequencies. To guarantee inductors behaviors at mm-wavefrequencies; it is important to achieve the quality factor peak beyondthe frequency of interest. To reduce all type of losses the top metal M6is chosen for all inductors. Furthermore; inductors L_(m), L_(e2),L_(d2), L_(d4), and the coupling transformer L_(ei), L_(b2), are allimplemented using microstrip transmission lines.

The stacked coupling transformer is shown in FIG. 8 where L_(e1) andL_(b2) consist of primary and secondary inductors; respectively. Thetransformer inverting configuration is implemented to form afeed-forward path boosting the transconductance gm₂ input stage. Allelectromagnetic effects from eddy current substrate loss to frequencydependent metal loss are considered in the design process of thetransformer.

In order to reduce the parasitic loss effect at high frequency; thestacked transformer is realized with the top metal layers M6 and M5which are the thickest and farthest from the substrate, thus reducinglosses. The quality factor and self-resonance frequency for both L_(ei)and L_(b2) remain almost identical. A high quality factor (Q) for thetransformer inductances is needed to reduce its noise contribution intothe balun-LNA structure.

For the optimal magnetic coupling between transformer conductors; themetal width for the microstrip transmission lines forming thetransformer are set to the smallest possible (7.5 μm) constrained by theohmic losses, the dc current, and the quality factor. The narrower theconductor dimensions width the higher the magnetic coupling between thetransformer turns. However; increasing the metal width leads to higherparasitic capacitance losses to the substrate.

The coupling coefficient, K, for the stacked transformer is limited bythe process technology due to metal thickness and minimum layers spacingas well as the optimal turn's ratio at mm-wave frequency. The benefitsand limitations of increasing the turn ratios for the stackedtransformer have been previously discussed. Thus, the stackedtransformer is designed with 1:1 turn's ratio. L_(e1) and L_(b2)inductances are 82 pH and 120 pH, respectively. A coupling coefficient;K equal to 0.34 is achieved in the band of interest.

FIG. 9 shows the EM simulations results of the transformer inductancesand the coupling coefficient. These parameters remain almost constant inthe frequency range of interest. This is because the self-resonancefrequency of the transformer is at higher frequency.

Simulation and Experimental Results

The wideband Balun-LNA embodiment was fabricated using 0.18 μm BiCMOStechnology from Tower Jazz Semiconductor [23].

FIG. 10 shows the die micrograph of the balun-LNA embodiment, where thetotal area is 0.46 mm² excluding the RF and DC pads. On-wafermeasurements were done using RF differential probes (G-S-G-S-G) forinput and outputs. The use of RF differential input probe is necessaryfor calibration purposes using Cascade Microtech Impedance StandardSubstrate (ISS) [24]. Although an RF differential probe is used at theinput, the input signal is fed into only one port. Also, a 6-pin DCprobe is used to provide the DC biasing. The balun-LNA core consumes 5mA from 1.8V supply.

FIG. 11 shows the measured and simulated input return losses (S₁₁) forthe balun-LNA. Measured S₁, is larger than 8.7 dB for the entireoperating frequency range of 22-35 GHz and up to 40 GHz.

FIG. 12 displays the measured and simulated output return losses S₂₂ andS₃₃. Measured S22 is better than 9 dB from 22-29 GHz and S₃₃ is largerthan 7.5 dB from 23.5-27.4 GHz. The shifting of the return lossresponses at the outputs of the balun-LNA is mainly due to thevariations of the small metal insulator metal (MIM) output capacitancesas well as the parasitic inductances coupling to the substrate.Consequently, the measured power gains for the balun-LNA (S₂₁ and S₃₁)shift to 26.8 GHz and 27 GHz, respectively, as seen in FIG. 13, whichshows S₂₁ and S₃₁ achieving a gain of 15.6 and 15.4 dB, respectively.This represents a measured differential gain boost of 2.0 dB and 2.4 dBfor S₃₁ and S₂₁ compared to simulations. The measured 3-dB bandwidthsfor S₂₁ and S₃₁ are 7.6 GHz and 11.5 GHz, respectively. A 3.9 GHzbandwidth difference between S₂₁ and S₃₁ is mainly due to asymmetricsignal path from input to outputs and unequal parasitic capacitances tothe substrate.

FIG. 14 shows the measured stability of the balun-LNA embodiment in termof the stability parameter μ [25], which is derived from the measuredS-parameters. The balun-LNA is unconditionally stable for both channelsacross the 22-35 GHz bandwidth according to μ(s)>1. The measured noisefigures for both channels are shown in FIG. 15, where the noise figuresbetween input port 1 and output port 3 (NF₃₁) and input port 1 andoutput port 2 (NF₂₁) vary from 4.5 dB to 5.8 dB and from 4.6 dB to 7.09dB, respectively. NF₂₁ experiences higher noise figure particularly dueto channel gain drop. In the case of a differential to single endedbalun applied at the output of the proposed balun-LNA, a 3-dBdifferential gain increase is possible and a much lower noise figure canbe achieved due to common mode noise cancellation.

The measured gain and phase imbalances are shown in FIG. 16. The gainand phase mismatches from 20-30 GHz are 1.8 dB and 12°, respectively.However, the gain mismatch can reach 5.5 dB at 35 GHz. The measurementsof the 1-dB power compression points (P1 dB₂₁ P1 dB₃₁) and the inputreferred third order intercept points (IIP3₂₁ and IIP3₃₁) for bothchannels for the frequency range of 22-35 GHz are shown in FIG. 17.

P1 dB and IIP3 higher than −14.8 and −6 dBm across 22-35 GHz areachieved for both channels, respectively. The performance of theproposed wideband balun-LNA is shown in Table I in comparison with otherLNA designs operating in the same frequency spectrum. These resultsconfirm that the balun-LNA exhibits good differential property, highpower gain, low noise figure, very competitive linearity, and the lowestpower consumption in the K/Ka-band of operation.

A wideband 22-35 GHz balun-LNA embodiment is implemented using −18 μm.SiGe BiCMOS technology. The balun-LNA structure implemented newlinearity technique based on Gm-constant approach and utilized couplingstaked transformer to improve power and noise efficiency. Analyticalexpressions for the wideband input matching impedance, linearity, noisefigure, and stability were developed to highlight the design tradeoffs.The gain and phase mismatches for the frequency range of 20-30 GHz are1.8 dB and 12° respectively. Power gains of 15.6 and 15.4 dB, 3-dBbandwidths of 7.6 GHz and 11.5 GHz, noise figures of 4.5-5.8 and4.6-7.09 dB, and linearity better than −6.07 dBm are achieved betweenthe input and two outputs. The balun-LNA consumes only 5 mA dc currentfrom 1.8V supply and having an active area of 0.46 mm².

Noise Analysis Basis

The noise analysis presented below is based on the noise model shown inFIG. 6. Before determining the input referred voltage noise due to thebase and collector shot currents of transistors Q₁, Q₂, we had to solvevarious circuits' impedances affected by the transformer behavior. Fromthe noise model, Z_(x) is the impedance looking from the base oftransistor Q₂ into the transformer. Similarly, Z_(c) is the impedance atthe collector of Q₁. Z_(M) is the impedance due to Miller effect attransistor Q₁. Further, Z_(e), and Z_(s) are the impedances looking atthe emitter and from the base into the source generator of Q₁,respectively. Applying KCL analysis yields Eqs. (A1)-(A5) as follows.

$\begin{matrix}{Z_{x} \approx {Z_{2}{{}\left\lbrack {R_{{bx}\; 2} + {sL}_{b\; 2} + \frac{({Kn}){{sL}_{e\; 1}\left( {{sL}_{b\; 2} + Z_{1} + Z_{2}} \right)}\left( {{sC}_{be} + g_{m\; 1}} \right)}{{g_{m\; 1}Z_{1}} - {({Kn}){{sL}_{e\; 1}\left( {{sC}_{be} + g_{m\; 1}} \right)}}} + Z_{1}} \right\rbrack}}} & ({A1})\end{matrix}$

where Z₁, Z₂ are defined earlier.

$\begin{matrix}{Z_{c} \approx {Z_{1}{{}\left\lbrack {{sL}_{b\; 2} + \frac{({Kn}){{sL}_{e\; 1}\left( {{sL}_{b\; 2} + Z_{1} + Z_{2}} \right)}\left( {{sC}_{be} + g_{m\; 1}} \right)}{{g_{m\; 1}Z_{1}} - {({Kn}){{sL}_{e\; 1}\left( {{sC}_{be} + g_{m\; 1}} \right)}}} + Z_{2}} \right\rbrack}}} & ({A2}) \\{{Z_{\mu} \approx {\left\lbrack Z_{c} \right\rbrack + \left( \frac{1}{{sC}_{bc}} \right)}}{Z_{M} \approx \left( \frac{Z_{\mu}}{\left( {1 - A_{v}} \right)} \right)}} & ({A3})\end{matrix}$

Where A is the voltage gain of the balun-LNA.

$\begin{matrix}{Z_{e} \approx {{sL}_{e\; 1}\left\lbrack {1 + \frac{({Kn})\left( {{g_{m\; 1}Z_{1}} - {({Kn}){{sL}_{e\; 1}\left( {{sC}_{be} + g_{m\; 1}} \right)}}} \right)}{\left( {{sL}_{b\; 2} + Z_{z} + Z_{2}} \right)\left( {{sC}_{be} + g_{m\; 1}} \right)}} \right\rbrack}} & ({A4}) \\{{Z_{s} \approx}❘\left( {R_{bx} + R_{L_{b}} + {sL}_{b} + \left( \frac{R_{s}}{{{sC}_{pad}R_{s}} + 1} \right)} \right)} & ({A5})\end{matrix}$

The base and collector current shot noises for transistors Q₁, Q₂ aregiven by:√{square root over (I ² _(n,b1,2))}=2qI _(B1,2)  (A6)√{square root over (I ² _(n,c1,2))}=2qI _(C1,2)  (A7)

where q is the electron charge constant, and I_(B1,2) and I_(C1,2) arethe collector and base currents for transistors Q₁, Q₂, respectively.

The input referred voltage noise due to the base and collector currentsshot noises of transistors Q₁ and Q₂ including the parasitic baseresistance R_(bx2) are shown in (A8)-(A12) where β is the current gainof Q₁ and Q₂.

$\begin{matrix}{\mspace{20mu}{\sqrt{\frac{v_{{ni},{Q\; 1}}^{2}}{\overset{\_}{i_{n,{c\; 1}}^{2}}}} \approx {{\left\lbrack {1 - \frac{Z_{e}}{Z_{e} + {\left( \frac{r_{e}}{{{sC}_{be}r_{e}} + 1} \right)\left( \frac{1}{B} \right)\left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right)}}} \right\rbrack\frac{1}{g_{m\; 1}}}}^{2}}} & ({A8}) \\{\mspace{20mu}{\sqrt{\frac{v_{{ni},{Q\; 1}}^{2}}{\overset{\_}{i_{n,{b\; 1}}^{2}}}} \approx {\begin{matrix}{{\left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right){}\left( {\left( \frac{\beta\; r_{e}}{{{sC}_{be}\beta\; r_{e}} + 1} \right) + {\beta\; Z_{e}}} \right)} +} \\{\frac{Z_{e}}{Z_{e} + \left( \frac{r_{e}}{{{sC}_{be}\; r_{e}} + 1} \right) + {\left( \frac{1}{\beta} \right)\left( \left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right) \right)}}\frac{1}{g_{m\; 1}}}\end{matrix}}^{2}}} & ({A9}) \\{\mspace{20mu}{\sqrt{\frac{v_{{ni},{Q\; 2}}^{2}}{\overset{\_}{R_{{bx}\; 2}^{2}}}} \approx {{\left\lbrack \frac{Z_{2}}{Z_{2} + Z_{x}} \right\rbrack\left\lbrack \frac{1}{\left( {\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right)} \right\rbrack}}^{2}}} & ({A10}) \\{{\sqrt{\frac{v_{{ni},{Q\; 2}}^{2}}{\overset{\_}{i_{n,{b\; 2}}^{2}}}}\quad} \approx {{\left\lbrack {\left( \frac{Z_{2}Z_{x}}{Z_{2} + Z_{s}} \right) + \frac{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2}} \right)}{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2}} \right) + \left( \frac{r_{e\; 2}}{{{sC}_{{be}\; 2}r_{e\; 2}} + 1} \right) + {\left( \frac{1}{\beta} \right)\left( \frac{Z_{x}}{{{sC}_{p\; 2}Z_{x}} + 1} \right)}}} \right\rbrack{\quad{\quad\left\lbrack \frac{1}{\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack }^{2}}}}} & ({A11}) \\{\sqrt{\frac{v_{{ni},{Q\; 2}}^{2}}{\overset{\_}{i_{n,{e\; 2}}^{2}}}} \approx {{\left\lbrack {1 - \left\lbrack \frac{R_{L_{e\; 2}}}{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2} + \left( \frac{r_{e\; 2}}{{{sC}_{{be}\; 2}r_{e\; 2}} + 1} \right)} \right) + {\left( \frac{1}{\beta} \right)\left( \frac{\left( {R_{{bx}\; 2} + Z_{x}} \right)}{{{sC}_{p\; 2}\left( {R_{{bx}\; 2} + Z_{x}} \right)} + 1} \right)}} \right\rbrack} \right\rbrack \cdot {\quad\left\lbrack \frac{1}{\frac{g_{m\; 1}}{g_{m\; 3}} + {nK}} \right\rbrack }_{2}}}} & ({A12})\end{matrix}$

Now, taking the outcomes from (A8)-(A12) and normalize it to the sourcegenerator impedance R_(s) results in (A13)-(A17). ψ₁(ω)-ψ₅(ω) is thetotal equivalent input referred voltage noise power shown in (14).

$\;\begin{matrix}{\mspace{20mu}{{\Psi_{1}(\omega)} \approx {\frac{1}{2R_{s}}{\left\lbrack {1 - \frac{Z_{e}}{Z_{e} + \left( \frac{r_{e}}{{{sC}_{be}r_{e}} + 1} \right) + {\left( \frac{1}{\beta} \right)\left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right)}}} \right\rbrack }^{2}}}} & ({A13}) \\{\mspace{20mu}{{\Psi_{2}(\omega)} \approx {\frac{1}{2\beta\; R_{s}}{\begin{matrix}{{\left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right){}\left( {\left( \frac{\beta\; r_{e}}{{{sC}_{be}\beta\; r_{e}} + 1} \right) + \left. \quad{\beta\; Z_{e}} \right)} \right)} +} \\\frac{Z_{e}}{Z_{e} + \left( \frac{r_{e}}{{{sC}_{be}r_{e}} + 1} \right) + {\left( \frac{1}{\beta} \right)\left( \left( \frac{Z_{M}Z_{s}}{Z_{M} + Z_{s}} \right) \right)}}\end{matrix}}^{2}}}} & ({A14}) \\{\mspace{20mu}{{\Psi_{3}(\omega)} \approx \frac{R_{{bx}\; 2}{\left\lbrack \frac{Z_{2}}{Z_{2} + Z_{x}} \right\rbrack }^{2}}{R_{s}}}} & ({A15}) \\{{\Psi_{4}(\omega)} \approx {\frac{1}{2\beta^{2}R_{s}}{\left\lbrack {\left( \frac{Z_{2}Z_{x}}{Z_{2} + Z_{x}} \right) + \frac{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2}} \right)}{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2}} \right) + \left( \frac{r_{e\; 2}}{{{sC}_{{be}\; 2}r_{e\; 2}} + 1} \right) + {\left( \frac{1}{\beta} \right)\left( \frac{Z_{x}}{{{sC}_{p\; 2}Z_{x}} + 1} \right)}}} \right\rbrack }^{2}}} & ({A16}) \\{{\Psi_{5}(\omega)} \approx {\frac{1}{2\beta^{2}R_{s}}{\left\lbrack {1 - \left\lbrack \frac{R_{L_{e\; 2}} + {sL}_{e\; 2}}{\left( {R_{L_{e\; 2}} + {sL}_{e\; 2} + \left( \frac{r_{e\; 2}}{{{sC}_{{br}\; 2}r_{e\; 2}} + 1} \right)} \right) + {\left( \frac{1}{\beta} \right)\left( \frac{\left( {R_{{bx}\; 2} + Z_{3}} \right)}{{{sC}_{p\; 2}\left( {R_{{bx}\; 2} + Z_{2}} \right)} + 1} \right)}} \right\rbrack} \right\rbrack }^{2}}} & ({A17})\end{matrix}$

Further Embodiments

With the ever growing consumers' demands for high data rate wirelesscommunications, bandwidth, and radar sensor devices are the main surgein the semiconductor market industry. Due to overcrowding on the lowerfrequency spectrum, the Federal Communications Commission (FCC) hasstandardized unlicensed microwave and millimeter-wave frequencies toserve the need [26]-[27]. To improve spectrum efficiency, the FCCauthorizes the ultra-wideband devices (UWB) to operate concurrently incoexistence with radio astronomy from 23.6-24 GHz,industrial-scientific-medical (ISM) from 24.05-24.25 GHz, IEEE 802.16standard for wireless metropolitan area network (WiMAN) ranging from10-66 GHz, short-range and long-range vehicular radar sensors forcollision avoidance from 22-29 GHz and from 77-81 GHz, and militaryradar sensor for unmanned aerial vehicle (UAV) at 35-37 GHz [3]. Thisfrequency spectrum allocation dilemma stems from the fact that these UWBdevices operate not only in coexistence with already standardizedadjacent bands, but it overlaps them. For that reason, the FCC regulatesthe effective isotropic radiated power (EIRP) for the UWB devices tolimit the interferences on the spectrum [26]-[27]. Transceiverstargeting microwave and mm-wave applications are reported with limitedagility using single-band approach [29]-[37], dual-band design[38]-[39], and lastly wideband RF front-end receivers [40]-[42].

Dedicated transceivers aiming for microwave and mm-wave specificapplications have come to light in recent years. A 0.18-μm 24 GHz CMOSRF front end was reported in [29]. An automotive short-range andlong-range radar sensor for Ka- and W-bands application with its FCCregulations was addressed in [30]-[31]. Various broadband architecturaltransceivers designs for the 60 GHz wireless communications are reportedin [32]-[34]. Such receivers with single-balanced RF mixers tend tosuffer from local oscillator (LO) leakage, thus causing receiverdesensitization. Fully integrated using 4 and 8 elements phased arrayreceivers in CMOS for 24 GHz ISM band are reported in [35]-[16].Further, a fully integrated 77 GHz BiCMOS phased array receiver withdipole antenna on chip for long-range automotive radar sensor isreported in [37].

To increase versatility and functionality, dual-bandtransceivers/receivers are demonstrated in [38]-[39]. Adding morepassive components to achieve dual-bands resonance introduces highsignal loss and increases chip area; hence, increases the powerconsumption. The dual-bands 24/31 GHz based sub-harmonic receiverarchitecture in [38] requires fine tuning for the quadrature phasesgeneration schemes as well for amplitude mismatches to improve bandsrejection. An automotive dual-bands direct conversion transceiver forcollision avoidance is reported in [39]. The large frequency spread ofthe transceiver frequency planning causes two dedicated localoscillators running at 22 and 77 GHz to be integrated on chip. Thedrawback is more power consumption, larger chip area, and more complexlayout floor planning not to mention the phase noise issues. As we cansee; single-band or dual-bands transceivers have limited flexibility.More desired approach targets multi-standards multi-bands using widebandRF front-end transceivers to increase functionality suffers from limitedlinearity [40]-[42].

A further embodiment for a wideband direct conversion current modereceiver for concurrently coexistent multi-standards multi-bands mm-waveapplications is discussed. The receiver consists of a main pathcorrelating the down converted output current gain stages into low inputimpedance of a trans-impedance amplifier (TIA) with a built-infeed-forward high-pass anti-aliasing blockers filter; no RF voltagegain. In addition, the auxiliary path utilizes an attenuator first blockproviding robustness to high power jamming UAV radar signals from 35-37GHz. The architectural receiver design concept is similar to [43]-[48]where current mode gain is maintained throughout the receiver RFfront-end. However, passive mixer increases the noise figure of thereceiver chain, thus a second gain stage is needed. A class AB amplifierwith low input impedance is added without limiting the receiverlinearity. Consequently, the class AB amplifier gain stage immunes thereceiver from I/Q interaction due to passive mixer 50% duty cycle [50].The direct conversion receiver is targeted to down convert all IEEEstandards within 22-44 GHz spectrum with 500 MHz baseband frequency (IF)bandwidth supporting UWB device applications. The wideband power localoscillator (LO) is provided from; R&S ZVA 67 GHz; vector networkanalyzer (VNA) with quad power sources and very acceptable phase noise.

Receiver Architecture Using the Low Noise Amplifier

A wideband versatile multi-standards multi-bands direct conversionreceiver chain for microwave and mm-wave coexistent applications 22-44GHz is shown in FIG. 18 using 0.18-μm BiCMOS technology.

The receiver architecture consists of a main path; and an auxiliary onededicated to high power jamming blocker for military unmanned aerialvehicle (UAV) radar application 35-37 GHz. The latter one is designed tohave an attenuator first block with linear phase characteristics. Areceiver signal strength indicator block (RSSI) senses the incomingantenna signal power level and controls path selectivity. The main pathconsists of a wideband active balun-LNA reported in [49] followed by alow input impedance class AB amplifier.

The differential current mode outputs of the two successive gain stagesare down-converted by an ac coupled doubly-balanced passive mixersthrough the correlation of differential In-phase/quadrature signalsusing quadrature all pass filter (QAP) design fed externally from adifferential local oscillator (LO). The cross-correlated current outputis converted to voltage using a feed-forward trans-impedance amplifier(TIA) with low input impedance. Furthermore; a feed-forward high-passpolyphase filter provides cancellation mechanism at the output TIA nodeand immune the receiver from out of band interferers (OBI), blockers,and reduce the effect of in-band aliasing. Note that the noisecontribution of this high-pass polyphase cancellation filter is minimalowing to its low gain frequency response in band. This design methodincreases receiver flexibility and functionality and reduces itsdependency on external duplexers and bulky MEMS filter as in [38].Hence, the bill of materials (BOM) is reduced. The proponents of theproposed receiver architecture including both paths are as follows:

-   -   1) Utilizing current mode amplification in the RF front-end, no        RF voltage gain. Thus, low noise figure (NF) and high in-band        linearity for the RF front-end is maintained.    -   2) Class AB amplifier with low input impedance preceded by a        highly linear balun-LNA bolsters the current amplification mode        without degrading the linearity compared to [43]; [45]; where        regular common source transconductance gm stages are used.    -   3) Having successive low input impedance throughout the        multi-gain stages of the RF front-end helps preserve the        wideband operation across the frequency band of interest, and        leads to less distortion in the mixer and the nonlinear output        impedances of the multi-gain current mode blocks. Hence, the        OBIs' experience no voltage gain amplifications and the first        voltage gain happens only at baseband after the low pass filter,        which provides channel filtering selectivity to mitigate the        OBI.    -   4) Having an active wideband single to differential balun-LNA        with asymmetric paths from input to outputs can causes amplitude        and phase mismatches due to unequal parasitics between the two        paths. To resolve this dilemma; single to differential passive        transformer is being used as part of the matching network for a        fully differential LNA [47]-[48].

However, a large insertion loss (<−4 dB) due to passive transformer isinevitable and technology dependent. Thus, the noise figure is degraded.The alternative approach is placing a differential class AB gain stageafter the balun-LNA to improve the common mode rejection and cancel anymismatches without linearity limitation. Furthermore; the class ABamplifier has built in amplitude and phase mismatches cancellationscheme. The architectural design advantages for this mm-wave receiverare ubiquitous. A more detailed analysis of these benefits is presentedbelow on the circuit implementation level.

Balun-LNA

A single to differential highly linear active wideband balun-LNA isdesigned to amplify the 22-44 GHz frequency spectrum. The architectureof the active balun-LNA has a wideband input matching network consistingof base inductance; L_(b); ac coupled transformer between L_(e1) andL_(b2), and coupling parasitic capacitances to the substrate as losses.The input matching response behavior is dependent on the couplingcoefficient; K; and the turn ratios between the transformer windings. Aresonant frequency shift is adjusted with the base inductance L_(b). Awideband performance is maintained due to low quality factor of thematching network through its poles and zeros cancellations. Yet, eachinductor must have a high quality factor with high self resonance tokeep the noise figure low. The output matching network consists ofinductive peaking capacitively coupled to the class AB amplifier withlow input impedance.

The balun-LNA architecture consists of two paths as follows; a maintransconductance gm gain stage path coupled to an auxiliary one using atransformer. The benefits of adding this transformer translates into anincrease in the signal to noise ratio (SNR) at the base-emitter junctionof the auxiliary path. Hence, a gain boost for less static dc power isachieved. Further; a lower input referred noise is seen in the auxiliarypath due to the transformer benefits. The 3-dB differential power gainS₂₁ is 15 dB and the bandwidth is limited by the return loss S₁₁<−10 dBacross the entire frequency band of interest. A linearity improvementtechnique is based on a constant G_(m)-cell transconductance behaviorfor the balun-LNA structure. The constant G_(m)-cell transconductance isestablished through equal emitters' area (A_(e)) ratios and properbase-emitter junction biasing. The constant small signal G_(m)-celltransconductance remains independent of input and output variationsunder large signal behavior. The proposed structure achieves a secondorder intermodulation (IM₂) cancellation, and the measured inputreferred third order intermodulation (IIP₃) and differential NF are >−1dB_(m) and <3.5 dB; respectively. The gain and phase mismatches are keptto a minimum. The total power consumption is less than 18 mW drawn froma 1.8V power supply.

Class AB Amplifier

The class AB amplifier is preceded with a highly linear current modebalun-LNA. Note that to maintain receiver chain linearity and suppressthe passive mixer noise contribution; a highly linear second gain stageamplifier is required. Current mode operation in RF front-end entailsnumerous benefits from noise to linearity; no RF voltage gain [43]-[45];[47]-[48]. To keep the voltage swing to a minimum at the input of theclass AB amplifier; a low differential input impedance has to bemaintained across the bandwidth of interest. The input impedanceconsists of the parallel combination of two sections. The first part ismade of the diode connected bipolar device Q_(2A) junction in serieswith inductor; L₂. The second part consists of the common base device QAin series with inductor; L₁. The derived input impedance of the class ABamplifier is based on the small signal model.

Equation (1) shows the derived input impedance below;

$\begin{matrix}{{Z_{{in},{AB}}(s)} = {{jwL} + \frac{V_{T}}{I_{C} + {V_{T}{sC}_{be}}}}} & (1)\end{matrix}$where we have the assumption I_(C1)=I_(C2)=I_(C), L₁=L₂=L, and V_(T) isthe thermal voltage. We also assumed the devices Q_(1A) and Q_(2A)emitter' area sizes are equal.

Further, the class AB amplifier architecture has a built-in cancelationmechanism for all phases and amplitudes mismatches generated from theasymmetry balun-LNA structure. Although the differential outputs of thebalun-LNA are evenly loaded, the input signal asymmetry path to theoutputs causes unequal coupling parasitic to the substrate, thus thephase and amplitude mismatches. To resolve this dilemma, the class ABamplifier on a single sided output consists of in-phase input currentbuffer combined with an out of phase current shifted (180°+α) to averagethe phase mismatches generated from the balun-LNA and the class ABamplifier. Once measuring the differential signal at the outputs of theclass AB amplifier, a complete phase error cancellation is possible intheory. However, the amplitude mismatch error is limited by the class ABamplifier output currents ratios. This partial amplitude errorcancellation can limit the phase error cancellation mechanism. Note thatthe phase and amplitude cancellation mechanism is independent of anypassive components and only limited by the active devices mismatches,thus the operation for the error cancellation mechanism is frequencyindependent and can reach well into the millimeter-wave frequencies.Simulations show phase and amplitude mismatches less than 1.7° and lessthan 0.5 dB, respectively across 0-45 GHz frequency band.

Passive Mixer and I/Q Generator

We use a simple model of the millimeter-wave direct conversion I/Qreceiver front-end using ac coupled fully balanced current-drivenquadrature passive mixers with 50% duty cycles. The 2 stages balun-LNAis a transconductor that supplies the RF current modeled by a currentsource and having load impedance Z_(L)(s). The second transconductancegain stage is a class AB amplifier with low differential inputimpedance, thus no RF voltage gain and the receiver linearity ismaintained. In addition, the proponents of the ac coupled second gainstage class AB amplifier to the passive mixers are not only limited tothe second order intermodulation product improvement, but also helpeliminate the I/Q channels crosstalk or interaction due to the lack ofreverse isolation between RF and baseband side of the passive mixer.This phenomenon is based on baseband voltage offset produced at theinput current buffer impedance; where an antiphase current image isgenerated from one set of switches to another cause I/Q interaction thataffect high and low sides mismatches of gain conversion, linearity(IIP2, IIP3), and noise figure of the current buffer [50]. Then, themajor problem with using 50% duty cycle approach has been resolved dueto the second class AB gain stage without sacrificing linearity.Furthermore, no dc current is commutating in the deeply trencheddual-well nMOS switches, thus the 1/f noise is greatly reduced at theinput current buffer.

The designer has control over the device's size and the LOcharacteristics. In the passive mixer increasing the device's size widthhelps reduce the switch on resistance, thus its thermal noisecontribution is lower. The dc biasing condition at the drain and sourceof the CMOS switch is set from the input current buffer impedance.Consequently, the dc bias voltage level of the LO signal is a paramountfactor in controlling the switches mode of operation. Thecharacteristics of the LO driver affects the performance of the mixer.Therefore, a large LO signal can help improve the passive mixerconversion gain as well its noise figure. In a 50% duty cycle fullybalanced passive mixer, the gain conversion is ideally equal to 2/Tr.However, if the switches of the quadrature passive mixer experience lessturn on time than off time then the conversion gain as well as the noisefigure are improved at the expense of less linearity.

An in-phase/quadrature phase generator is placed in the LO signal pathdue to relatively high insertion loss. Alternatively, the QAP can beplaced the RF signal path however, the tradeoffs between gain and noisefigure are to be considered. The simulations results for QAP in thefrequency range 22-44 GHz show an insertion loss of 13 dB within-phase/quadrature amplitude and phase mismatches less than 1.8 dB and±3, respectively. The tradeoff is between keeping low insertion lossversus maintaining flat phase response. The total LO power requirementfor the passive mixer is 15 dBm using a switch on resistance of 40Ω.From the combination of the LO power signal and the switches sizes, thequadrature passive mixer reaches an acceptable 4 dB noise figure with nopower consumption.

TIA with Out of Band Interferes Rejection Filter

A feed-forward trans-impedance amplifier (TIA) also known as open loopTIA is deployed to convert the down converted correlated output currentfrom the in-phase/quadrature passive mixers into voltages at thedifferential outputs of the TIA. Furthermore, an auxiliary path uses afeed-forward high pass polyphase filter (HPF) to reject blockers and LOharmonics leakage due to direct conversion receiver architecture. Notethe importance of 3^(rd) and 5^(th) LO harmonics rejection that causeintermodulation with blockers and interferes to down convert to UWBbaseband. Also, a buffer for dc interface is implemented to isolatebetween the TIA input impedance and the active HPF with no phase andamplitude changes. C_(L), C_(in) are designated as the total load andtotal input capacitances, respectively. The trans-impedance transferfunction is defined as:

$\begin{matrix}{{Z_{T}(s)} = {\frac{R_{T}}{\left( {1 + {s/\omega_{p\; 1}}} \right)\left( {1 + {s/\omega_{p\; 2}}} \right)} \cdot \left\lbrack \left( {1 - {\left( \frac{s/\omega_{p\; 3}}{{s/\omega_{p\; 3}} + 1} \right)\left( \frac{{sgm}_{2}C_{s}}{{sC}_{s} + {gm}_{2}} \right)}} \right) \right\rbrack}} & (2)\end{matrix}$where R_(T) is defined as the output impedance of the TIA. Polesω_(p1)=gm₁/C_(in) and ω_(p2)=1/Z_(T)C_(L) are designated as the dominantand non-dominant poles for the feed-forward TIA, respectively.

For the open loop TIA and the feed-forward auxiliary cancellation pathtransconductances, gm₁ and gm₂ are set equals. The active HPF ispreceded by a coarse first order non-evasive HPF withω_(p3)=1/C_(dec)R_(bias). The active HPF is established using acapacitively degenerated common source stage. A fourth order HPF is seenat the differential output of the feed-forward TIA. Higher order of thefeed-forward cancellation filter can be easily implemented throughmulti-cascaded HPF stages at the expense of greater in-band noisefigure. Note that in the case of desirable reconfigurable bandwidth tosupport various IEEE standards, the degenerated capacitance at the HPFis bit controlled through an encoder to change its poles and zeros'location so as to maintain the same attenuation factor. Furthermore, theoutput impedance of the TIA has to incorporate a parallel conductancewith variable bias control as to trade the trans-impedance gain for thebandwidth. From simulation results, the trans-impedance gain is 55 dBΩwith 500 MHz bandwidth with no stability issues in accordance withminimum UWB requirements. In addition, the open loop TIA achieves 20 dBattenuations of the third harmonic tone at 1.5 GHz. The total systempower consumption is 18.6 mA drawn from a 1.8V supply.

When used in this specification and claims, the terms “comprises” and“comprising” and variations thereof mean that the specified features,steps or integers are included. The terms are not to be interpreted toexclude the presence of other features, steps or components.

The features disclosed in the foregoing description, or the followingclaims, or the accompanying drawings, expressed in their specific formsor in terms of a means for performing the disclosed function, or amethod or process for attaining the disclosed result, as appropriate,may, separately, or in any combination of such features, be utilised forrealising the invention in diverse forms thereof.

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The invention claimed is:
 1. An amplifier for signal amplification, theamplifier comprising: a signal input arrangement; a signal outputarrangement; a first transistor; a second transistor; a first inductorcoupled to an emitter of the first transistor; a second inductor coupledbetween a collector of the first transistor and a base of the secondtransistor, wherein the first inductor and the second inductor arearranged to operate respectively as a first coil of a transformer and asecond coil of the transformer; and a third transistor, wherein: thefirst, second and third transistors are coupled to one another to form atransconductance cell, the transconductance cell is coupled to thesignal input arrangement and the signal output arrangement, and thetransconductance cell is operable to receive a first signal from thesignal input arrangement, amplify the first signal and output anamplified first signal to the signal output arrangement.
 2. Theamplifier of claim 1, wherein the transconductance cell is configuredwith a collector terminal of the first transistor coupled to a baseterminal of the second transistor and an emitter terminal of the thirdtransistor.
 3. The amplifier of claim 1, wherein the transformer isconfigured to perform at least one of increasing the voltage gain of theamplifier and increasing a signal bandwidth of the amplifier.
 4. Theamplifier of claim 3, wherein the signal input arrangement comprises animpedance matching circuit which is coupled to the first transistor, theimpedance matching circuit comprising the first inductor and a thirdinductor each coupled to a base of the first transistor.
 5. Theamplifier of claim 1, further comprising: a fourth inductor coupledbetween an emitter of the third transistor and a collector of the firsttransistor.
 6. The amplifier of claim 1, wherein a collector of thesecond transistor is coupled to the emitter of a fourth transistor, andwherein the first, second, third and fourth transistors are arranged ina common-emitter configuration.
 7. The amplifier of claim 1, wherein abase of the third transistor, a base of a fourth transistor and a powersupply input are coupled to one another.
 8. The amplifier of claim 7,wherein the signal output arrangement comprises: a first output portioncoupled to a collector of the third transistor; and a second outputportion coupled to a collector of the fourth transistor.
 9. Theamplifier of claim 8, wherein the first output portion includes a firstpair of series connected inductors and a first output terminal coupledto the connection between the first pair of inductors, and wherein thesecond output portion includes a second pair of series connectedinductors and a second output terminal coupled to the connection betweenthe second pair of inductors.
 10. The amplifier of claim 9, furthercomprising: a first resistor coupled between the first output portionand the power supply input; and a second resistor coupled between thesecond output portion and the power supply input.
 11. The amplifier ofclaim 9, wherein the inductance of the first pair of inductors is equalto the inductance of the second pair of inductors.
 12. The amplifier ofclaim 10, wherein the amplifier is configured to be operable with apassive mixer and a trans-impedance amplifier and the signal outputarrangement is coupled to a class AB amplifier.
 13. The amplifier ofclaim 1, wherein the first signal comprises at least one signal having afrequency of 22 GHz to 35 GHz.
 14. The amplifier of claim 1, wherein theamplifier is constructed using a SiGe BiCMOS process.
 15. A method ofoperating an amplifier including a signal input arrangement, a signaloutput arrangement, a first transistor, a second transistor, and a thirdtransistor, a first inductor coupled to an emitter of the firsttransistor, a second inductor coupled between a collector of the firsttransistor and a base of the second transistor, wherein the firstinductor and the second inductor are arranged to operate respectively asa first coil of a transformer and a second coil of the transformer, themethod comprising: receiving, by a transconductance cell, a first signalfrom the signal input arrangement; amplifying the first signal; andoutputting an amplified first signal to the signal output arrangement,wherein the first, second and third transistors are coupled to oneanother to form the transconductance cell, the transconductance cell iscoupled to the signal input arrangement and the signal outputarrangement, and the transconductance cell is operable to receive afirst signal from the signal input arrangement, amplify the first signaland output an amplified first signal to the signal output arrangement.